Which two statements about conditional probability are true?

A researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic

Delvig [45]

Answer:

90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

Step-by-step explanation:

We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.

Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean iron concentration = 0.802 cc/cubic meter

s = sample standard deviation = 0.093

n = number of water samples = 27

$\mu$ = population mean

<em>Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.706 < $t_2_6$ < 1.706) = 0.90 {As the critical value of t at 26 degree of

freedom are -1.706 & 1.706 with P = 5%}

P(-1.706 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.706) = 0.90

P( $-1.706 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.706 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ) = 0.90

<u>90% confidence interval for</u> $\mu$ = [ $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ]

= [ $0.802 -1.706 \times {\frac{0.093}{\sqrt{27} }$ , $0.802 +1.706 \times {\frac{0.093}{\sqrt{27} }$ ]

= [0.771 , 0.832]

Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

4 0

2 years ago

Can you help me with this!!!!!!!!!

alexira [117]

a. The first variable is x and the second variable is y.

b. The equations are $x+y=12$ and $x-y=8.$

Step-by-step explanation:

Step 1:

The first step is to define the variables. The variables can be any two symbols, letters, characters, etc.

Here let the first variable be x and the let the second variable be y.

So the variables are defined as x and y.

Step 2:

The sum of the given variables is 12.

The first variable + the second variable = 12,

$x+y=12.$

The difference between the two variables is 4.

The first variable - the second variable = 4.

$x-y=4.$

Step 3:

If we add both the equations we get, $2x =16, x= 8$ and $y=4.$

x = 8 and y = 4.

4 0

2 years ago

Please help me :)), do not 'troll' with answers, it's graded...

wolverine [178]

The first one, decreasing then increasing

4 0

2 years ago

What transformations change the graph of f(x) to the graph of g(x)?

Dennis_Churaev [7]

For this case we have that the main function is given by:

$f (x) = - 7x ^ 2$

We apply the following transformations:

Vertical expansions:

To graph y = a * f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

For a = 5 we have:

$h (x) = 5 * f (x)\\h (x) = 5 * (- 7x ^ 2)\\h (x) = - 35x ^ 2$

Vertical translations:

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

For k = 5 we have:

$g (x) = h (x) + k\\g (x) = - 35x ^ 2 + 5$

Answer:

The graph of g (x) is the graph of f (x) stretched vertically by a factor of 5 and translated up 5 units.

3 0

2 years ago

Read 2 more answers

Name two different numbers that round to 30 when rounded to the nearest ten

andrew11 [14]

For this case we have the following definition:

tens place: number of two digits whose absolute value is greater than zero.

Then, we have the following rounding rule:

If the previous number is greater than or equal to five, the next number increases by one unit.

We then have the following numbers rounded to 30 when rounded to the nearest ten:

26: twenty-six

27: twenty-seven

Answer:

two different numbers that round to 30 when rounded to the nearest ten are:

26: twenty-six

27: twenty-seven

6 0

2 years ago

Read 2 more answers